The present invention relates to the field of three-dimensional prototype modeling. Specifically, it relates to a method of producing a prototype model having a set non-zero porosity determined by the type of packing pattern used to build the part.
To build an acceptable part, placement of sequentially applied material must currently be tightly controlled, because any errors in its placement will create dimensional errors that propagate throughout the part. Further, it is very difficult to accurately determine the impact of material placement errors at one layer on the accuracy of different layers of an article.
In ideal conditions for three-dimensional prototype modeling using continuous element deposition, if a deposition gun or extrusion head extrudes a bead of uniform area A at all extrusion speeds and if the bead trajectories are designed so that the beads have a horizontal spacing between them of "b" and a vertical spacing between them of "a," and A=ab, then a part having the proper dimensions will be produced. In discrete element deposition, if a deposition jet deposits droplets of volume V and the impact locations have a horizontal spacing between them of "b" and "c" and a vertical spacing of "a", then if V=abc, a part having the proper dimensions will be produced.
However, ideal conditions rarely exist, and numerous problems with accuracy of solid part dimensions are introduced into rapid prototyping processes. For example in continuous bead deposition, if a displacement pump is not used, the amount of material extruded per unit time depends non-linearly on the rate at which the pump is operated. In both continuous and discrete element deposition, in areas of high surface curvature physical characteristics of the material cause gaps between the beads; these physical characteristics include internal viscosity, surface tension, and rapid solidification.
In continuous bead extrusion rapid prototyping, there are two limiting cases for packing patterns for beads: rectangular and hexagonal. In a rectangular packing, the bead material must flow into 90 degree corners having infinitesimal radii to completely fill the volume. Problems occur in hexagonal packing, where the corners are 120 degrees. Beads are typically too viscous to fill in the 120 degree corners.
Another problem is that extrusion material varies from batch to batch. Further, material changes characteristics as it sits in a heated pot, because of absorption of and reaction with such things as water and oxygen from the air. All of the effects on the batches tend to cause the amount of material extruded in a bead or droplet at given pump speed to vary not only between batches, but also within batches.
Still another problem is that errors introduced into parts tend to propagate through the parts. Any error in a part, such as a lag or an excess of extrudate, will recur on all subsequent layers if the material is metered exactly. If a similar error occurs adjacent the first, the problem may even get worse in subsequent layers.
Extruded beads also change after extrusion. In continuous extrusion the material contracts as it cools; in addition beads contract axially and expand radially after being forced through the nozzle. For all of the above mentioned reasons, it is difficult to define exactly what the volumetric extrusion rate for a three-dimensional prototype modeling system is at any given time. It is also difficult to determine how one bead layer will lay on the next, due to the inherent uncertainty in the base layer.
There are several types of prototyping currently in use. Continuous extrusion based rapid prototyping involves depositing segments of continuous roads, ribbons, or beads of material onto a platform to sequentially build up an object. A cross section in a vertical plane of a number of such locally parallel beads normal to their axis will find that there are two limiting cases for how they can be packed together, namely in a rectangular array or in an hexagonal array. In the first case a longitudinal gap or pore tends to form along the line where four beads are nearest neighbors, and in the second case the pore forms along the line where three beads are nearest neighbors.
Lamination based rapid prototyping involves depositing shaped sheets or films to sequentially build up a solid object. Nominally these sheets join on continuous planes so that porosity is not necessarily present. Texturing the sheets with grooves or holes will introduce porosity that will help in lost wax casting applications, as described in the subsequent section. With this exception, parts manufactured with sheet laminations generally have zero porosity.
Discrete element extrusion based rapid prototyping involves depositing droplets or particles of material from a nozzle or projector so that the droplets sequentially build up a solid object. A cross section through such an object from any direction will show voids of some size at the locations where three, four, or even more droplets are nearest neighbors.
The techniques that we will subsequently describe for controlling rapid prototyping processes can be applied to several existing technologies. A brief review of these technologies shows that their practitioners have not realized the benefits of deliberately introducing porosity, especially at optimal levels.
For example, Batchelder et al. (U.S. Pat. No. 5,303,141) is silent on the role of part porosity. FIGS. 9a-9c of Batchelder et al. depict beads deposited at the maximum possible porosity (cylindrical beads in line contact with their neighbors), which is not the preferred embodiment for practical part building.
Fujimaki et al. (Japan application 62-234910) shows a solid object being constructed from spherical particles in FIG. 4 and in the supporting text. Such a part has a greater porosity than is recommended. FIG. 4 shows a body centered cubic lattice of spheres creating the object, which would have a porosity of almost 45%. Each sphere would have only a point contact with its six nearest neighbors, which would create a weak part. FIGS. 6a and 6b show other part cross sections, where again the parts seem to be comprised of spheres in point contact.
Masters (U.S. Pat. No. 4,665,492) shows in FIGS. 2a-2c that material deposited by ink jet like mechanisms will have some residual porosity, but is silent on the importance or optimization of that porosity.
The patents to Sachs et al. (U.S. Pat. Nos. 5,204,055 and 5,340,656) apply binder with an ink jet to a powder to make three dimensional parts. While there is an assumption that the powders are porous so that the binder fluid will wick into the powder, the patent is silent on any role or importance of porosity.